Standard Deviation Calculator
Sample and population spread, variance and standard error.
Enter your values
Enter the data (comma separated) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Sample standard deviation
- 2.160247
- Population standard deviation
- 2
- Sample variance
- 4.666667
- Mean
- 6
- Standard error of the mean
- 0.816497
Working
- 1n = 7, Σ(x − x̄)² = 28
Quick answer
Standard deviation measures average distance from the mean; sample SD divides by n−1, population SD by n.
s = √(Σ(x − x̄)² ÷ (n − 1))
At a glance
| What it does | Sample and population spread, variance and standard error. |
|---|---|
| Category | Statistics |
| Inputs needed | Data (comma separated) |
| Main output | Sample standard deviation |
| Formula | s = √(Σ(x − x̄)² ÷ (n − 1)) |
| Cost | Free — no sign-up, no download |
How to use the Standard Deviation Calculator
- 1Paste your data separated by commas.
- 2Use sample SD for a sample, population SD for a full population.
- 3Read variance and standard error too.
Inputs explained
- Data (comma separated)
- Enter the data (comma separated) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Data (comma separated)4, 8, 6, 5, 3, 9, 7
Results
- Sample standard deviation2.160247
- Population standard deviation2
- Sample variance4.666667
- Mean6
- Standard error of the mean0.816497
- n = 7, Σ(x − x̄)² = 28
Frequently asked questions
Why divide by n − 1?
Bessel's correction. A sample mean sits closer to its own data than the true mean, so dividing by n underestimates the spread.
What does one SD mean?
In a normal distribution, about 68% of values fall within one standard deviation of the mean.
What do I need to enter into the Standard Deviation Calculator?
Just 1 value: data (comma separated). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Standard Deviation Calculator work out the answer?
Standard deviation measures average distance from the mean; sample SD divides by n−1, population SD by n. It applies the formula s = √(Σ(x − x̄)² ÷ (n − 1)) and shows the working so you can check each step by hand.
Is the Standard Deviation Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.